Method and apparatus for improving performance of AC machines

ABSTRACT

A method and apparatus for improving the performance of polyphase AC machines. The polyphase AC machines are excited both with a fundamental frequency and with an odd harmonic of the fundamental frequency. The fundamental flux wave and the harmonic flux wave will travel at synchronous speed in the air gap. This facilitates redistributing the flux densities in the machine and thereby increasing the total flux per pole in the machine.

This is a continuation of co-pending application Ser. No. 888,818 filedon Jul. 22, 1986, now abandoned.

BACKGROUND OF THE INVENTION

The present invention relates generally to methods and apparatus forimproving the performance of alternating current (AC) machines, and morespecifically relates to methods and apparatus for improving theperformance of polyphase AC machines through the injection of harmonicfrequencies into the excitation current.

With conventional polyphase AC machines, both induction and synchronous,the machines are typically operated by a single frequency source. Themachines have armature windings to which the single frequency sine wavesare applied. The ideal performance of conventional polyphase AC machineswould include a sinusoidal air-gap flux wave of constant amplituderotating around the air-gap at synchronous speed. In this theoretical,ideal polyphase AC machine, the constant amplitude flux wave willproduce a constant electromagnetic torque. The torque of the machine ismonotonically dependent upon this constant amplitude flux wave. Thisideal situation may be approximated in large scale machines.

In conventional AC machines the magnetic flux per pole of the machine isproportional to the area of 1/2 sine wave of the air-gap flux wave ofthe machine. Typically, a conventional AC machine is designed to operatewith at least one of the magnetic members, the iron cores or teeth, ofthe machine in flux saturation. In conventional machines, the saturationflux densities of the iron, or other magnetic members, of the stator androtor determine the maximum amplitude of the air-gap flux wave. Inconventional machines, therefore, the amplitude of the fundamental fluxsine wave determines the maximum power output of the machine. This istrue even though maximum use is not made of all of the flux capabilityof the magnetic members.

In conventional AC machines, undesirable space harmonics are typicallyestablished in the air-gap flux waves. These naturally-arising spaceharmonics occur as a function of the particular machine design whenexcited by a fundamental frequency. Factors such as slots in themachines and core saturation contribute to the generation of theseundesirable space harmonics. These space harmonic flux waves areundesirable because they typically rotate in the air-gap at speeds otherthan that at which the fundamental flux wave rotates. Additionally, thespace harmonic flux waves can be travelling in either a forward orbackward direction, as well as at different speeds, relative to thefundamental flux wave. For example, a naturally-arising fifth spaceharmonic flux wave will travel in a reverse direction relative to thefundamental flux wave and will travel at 1/5 the speed of thefundamental flux wave. Similarly, a naturally-arising seventh spaceharmonic flux wave will travel in the same direction as the fundamentalflux wave, but at 1/7 the speed. These space harmonic flux waves caninteract with the squirrel cage winding in an induction motor, or withthe damper winding in a synchronous motor, to produce a braking torquewhich reduces the useful output of the machine. Additionally, thesenaturally-generated space harmonic flux waves can interact with eachother, and with the fundamental flux wave, to cause pulsations in thetorque of the machine, as well as unwanted mechanical vibrations.

Accordingly, the present invention provides a new method and apparatusfor constructing and operating a polyphase AC machine whereby a harmonicflux wave will travel in the same direction, and at the same(synchronous) speed, as the fundamental flux wave and whereby thefundamental flux wave is augmented in response to the harmonic flux waveso as to achieve improved electromagnetic loading in the magnetic pathof the machine; both achievements serving to improve the useful outputof a given machine.

SUMMARY OF THE INVENTION

The methods and apparatus of the present invention improve theperformance of polyphase AC machines through excitation of the machinewith frequencies which are odd harmonics of the fundamental excitationfrequency. This odd harmonic excitation serves to improve performance ofthe machine in two ways: (a) the flux distribution caused by theharmonic excitation enables a greater fundamental flux distribution andthereby yields an improved total flux distribution in the magnetic pathof the machine, thereby causing improved magnetic loading of thematerial, and (b) if the other conductors on the machine (typically onthe rotor) contain conductors or coils responsive to the harmonicfrequencies applied to the armature, or if the pole shape of the rotorproduces a permeance wave responsive to the harmonic frequencies, theharmonic flux distributions themselves will yield increased torque inthe machine.

As will be discussed in more detail later herein, this odd harmonicexcitation can be practiced in a variety of ways, including: separatecoils for fundamental excitation and for each odd harmonic excitation;multiphase power supplies for both fundamental and harmonic frequenciescoupled to a common winding; the use of a multiplicity ofdelta-connected windings coupled to one another through volt-ampbalancers, with separate phases of the harmonic excitation currentapplied to each delta; and a common set of delta-connected windingsactuated through use of a multiphase inverter, with a separate phase ofthe harmonic excitation current applied to each delta.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-D graphically depict the flux distribution in a section of themagnetic path of an AC machine. FIG. 1A depicts a sinusoidal fluxdistribution. FIG. 1B depicts a square wave flux distribution. FIG. 1Cdepicts a total flux distribution achieved by adding an increased levelof fundamental flux distribution with a third harmonic fluxdistribution. FIG. 1D depicts a total flux distribution achieved byadding a further increased fundamental flux distribution with third andfifth harmonic flux distributions.

FIGS. 2A-C graphically depict the flux distributions in differentportions of an AC machine. FIG. 2A depicts the flux distributions withthe machine operated with neither of the magnetic members in saturation.FIG. 2B depicts how the flux distributions in a typical low speedmachine can be adjusted through practice of the present invention toimprove machine performance. FIG. 2C depicts how the flux distributionsin a typical high speed machine can be adjusted through practice of thepresent invention to improve machine performance.

FIG. 3 graphically depicts the relationship between the ratio of thefundamental flux density to the maximum design flux density of a machineand the ratio of the third harmonic flux density to the maximum designflux density of the machine.

FIG. 4 schematically depicts the phase belts for a machine in accordancewith the present invention having separate windings for fundamental,third harmonic and fifth harmonic frequencies and power supplies forexciting such machine.

FIG. 5 schematically depicts a single layer winding for a machine inaccordance with the present invention to be excited through combinedfundamental and third harmonic power sources.

FIG. 6 depicts the power source connections to the machine of FIG. 5.

FIG. 7 schematically depicts a machine in accordance with the presentinvention having double layer windings with a per-unit pitch of lessthan 1.

FIG. 8 depicts the connections and the back emf potential points for amachine when such machine is excited through use of volt-amp balancers.

FIG. 9 depicts the slot electrical connections for a machine to beexcited as in FIG. 8.

FIG. 10 schematically depicts the connections for the machine of FIGS.8-9.

FIG. 11 depicts the fundamental frequency back emf voltage differencesbetween harmonic phases found in alternate slots in the machine of FIGS.8-10.

FIG. 12 schematically depicts a machine with 60° phase belt connectionsfor excitation through use of volt-amp balancers.

FIG. 13 schematically depicts the electrical connections for the machineof FIG. 12.

FIG. 14 schematically depicts the windings of an alternative embodimentof a machine to be excited through use of volt-amp balancers.

FIG. 15 schematically depicts the connections and the fundamentalfrequency back emf potential points for the machine of FIG. 14.

FIG. 16 schematically depicts the electrical connections for the machineof FIGS. 14 and 15.

FIG. 17 schematically depicts the winding configuration for the armatureof a machine to be excited through use of a multiphase inverter.

FIG. 18 schematically depicts the windings of the machine of FIG. 17.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention utilizes the injection of harmonic frequenciesinto the excitation current of a polyphase AC machine to optimize theflux densities in both the iron portions and the air-gap of the machine.Those skilled in the art will recognize that the resulting increase intotal flux in the machine will yield improved performance of themachine.

Referring first to FIGS. 1A-D of the drawings, each Figure graphicallydepicts the total flux distribution in a section of the magnetic path ofan AC machine under different conditions. The ordinate of each graph isthe phase angle while the abscissa represents the ratio of the localflux distribution (B) to the maximum design flux density (B_(S)) in themachine.

FIG. 1A depicts a sinusoidal flux distribution 10 in the magnetic path,resulting from a sinusoidal excitation current. Flux distribution 10 hasa peak amplitude 12. FIG. 1B depicts a square wave flux distribution 14having an amplitude 16 equal to the peak amplitude 12 of sinusoidaldistribution 10 in FIG. 1A. The theoretical flux per pole of a machineactuated with the square wave flux distribution 14 of FIG. 1B is 1.57times the flux per pole of a machine actuated by sinusoidal distribution10 of FIG. 1A. Such a theoretical machine would make optimal usage ofthe flux capacity of the iron portions of the machine. Square waves,however, cannot be produced in practical machines because practicalpower supplies are not available.

A square wave can be synthesized by an infinite set of odd harmonics.Although such synthesization is impractical, a square wave can beapproximated by a finite set of odd harmonics. FIG. 1C depicts a fluxdistribution 18 achieved by adding an increased fundamental fluxdistribution 19 to the flux distribution of the third harmonic 20. Theflux per pole of flux distribution 18 is 1.23 times that of thesinusoidal flux distribution 10 resulting from only fundamentalexcitation.

FIG. 1D depicts a flux distribution 22 achieved by adding a furtherincreased fundamental flux distribution 21 to an increased thirdharmonic flux distribution 23 and a fifth harmonic flux distribution 24.The flux per pole of flux distribution 22 is 1.31 times that ofsinusoidal flux distribution 10.

Additional correlated odd harmonic flux distributions will allow furtherincreases in the relative flux per pole relative to a sinusoidal fluxdistribution 10 resulting from fundamental excitation only. The furtheraddition of these odd harmonic flux distributions will approach the fluxper pole of square wave flux distribution 14. However, additional oddharmonic flux distributions will yield smaller incremental changes thanthose provided by the addition of the third and fifth harmonics asdepicted in FIGS. 1C and 1D. The addition of the third harmonic fluxdistribution facilitates the greatest increase in the total fluxdistribution and will therefore be discussed here in the greatestdetail.

Referring now to FIGS. 2A-C, graphically depicted in each figure are thecore flux distributions 25a, 25b, and 25c in respective figures, and theteeth and gap flux distributions, 27a, 27b and 27c in respectivefigures, in a machine under three different conditions. Conventionalpractice in the design of polyphase AC machines is to design the fluxdensities in the stator core, the stator teeth, the rotor core and therotor teeth in such a way as to avoid excessive flux saturation in anyparticular section. This practice serves to limit magnetization currentand core loses to acceptable values. The air-gap flux distribution canbe other than a sinusoidal wave form, distortion in the distributionbeing largely dependent upon the degree of saturation in the magneticpaths.

FIG. 2A depicts the core flux distribution 25a, and the teeth and gapflux distribution 27a of a machine wherein neither section of themachine is saturated. Each flux distribution is a sinusoid in responseto the fundamental frequency excitation. Core flux distribution 25a isderived from integration of teeth and gap flux distribution 27a, and istherefore 90° apart in space from teeth and gap flux distribution 27a.

In reality, a machine will be operated with at least one section of themachine approaching saturation. Further, the degree of saturation indifferent magnetic paths cannot be totally equal. For example, in a lowspeed machine having a large number of poles, flux densities in thestator and rotor cores are much lower than the flux densities in thestator and rotor teeth. The reason is that the minimum dimension of eachcore is determined by mechanical requirements, such as rigidity, stress,and manufacturing requirements; but is not determined by electromagneticrequirements. Saturation of the teeth is therefore a determining factorfor how much flux per pole can be produced in the machine. Conversely,for high speed machines, such as two pole machines, the core sectionsare typically more saturated than the teeth sections.

The performance, and therefore the rating, of an AC machine is dependentupon the total flux per pole that can be produced in the machine. Thepresent invention facilitates the total flux per pole in a polyphase ACmachine to be increased by maintaining or lowering flux density in onemagnetic path while increasing the flux density in another magneticpath. This redistributing of the flux is accomplished by adjusting thephases of the harmonic excitation relative to the fundamentalexcitation. For example, FIG. 2B depicts exemplary flux distributionscontemplated through use of the present invention in a low speed machineas discussed above. The density of the core flux 27b is increasedthrough use of fundamental flux distribution 28 and third harmonic flux20 distribution 29. At the same time, however, the density of teeth andgap flux 27b is decreased relative to fundamental flux distribution 28and third harmonic flux distribution 29. The injection of third harmonicexcitation current to establish third harmonic flux distribution 29,therefore, facilitates increasing the density of the core flux 25b whiledecreasing the density of teeth and gap flux distribution 27b, moreevenly distributing the flux in the machine, and, most importantly,facilitating an increase in the total flux per pole in the machine.

FIG. 2C, depicts exemplary flux distributions contemplated through useof the present invention with a high speed machine as discussed above.In FIG. 2C, the phase angle of third harmonic flux distribution 29' hasbeen changed relative to fundamental flux distribution 28'. This resultsin a decrease in the density of core flux 25c and facilitates anincrease in teeth and gap flux 27c. This again promotes a more even fluxwithin the machine and facilitates an increased total flux per pole inthe machine.

Referring now to FIG. 3, therein is graphically depicted, by a curve 31,the relationship between the fundamental flux density and the thirdharmonic flux density in a machine. The abscissa of the graph of FIG. 3represents the ratio of the fundamental flux density to the maximumdesign flux density of a machine, while the ordinate represents theratio of the third harmonic flux density to the maximum design fluxdensity of the machine. The relation expressed in curve 31 assumes thatthe total flux density in the machine remains unchanged.

In determining the relative amplitudes for the fundamental and thirdharmonic excitation voltages, the maximum third harmonic voltage shouldbe applied which will facilitate the maximum fundamental voltage whichcan be applied which will improve machine performance without exceedingthe thermal rating of the machine. In addition to this primaryparameter, however, the actual ratio between the fundamental and thirdharmonic excitation voltages may be affected by secondary factors, suchas changes in core losses due to the excitation by both fundamental andthird harmonic frequencies, or changes in deleteriousnaturally-occurring space harmonics as discussed earlier herein, etc.The amplitude and the relative phases of all excitations will be in syncso as to produce optimal flux densities as discussed earlier herein.

Following is a discussion of increased performance of different types ofAC machines through use of the present invention. With respect to any ofthe below discussed polyphase AC machines, because harmonic sinusoids ofdifferent frequencies are orthogonal, the fundamental and each harmonicof the stator-produced flux wave will interact to produce torque onlywith its counterpart in the rotor produced flux wave.

The benefits of the present invention may be achieved with differenttypes of AC machines including, for example: squirrel cage inductionmotors, wound rotor induction motors, and both salient pole and roundrotor synchronous machines. Different practical considerations withrespect to the present invention will be found with these differentmachines, however. A squirrel cage induction motor will experienceenhanced torque production from the increased fundamental componentfacilitated through harmonic injection, as depicted in FIGS. 1C and 1D.Additionally, a squirrel cage induction motor will experience enhancedtorque production from each harmonic flux component provided that theconductors forming the squirrel cage on the rotor are finely enoughdivided to allow each space harmonic of induced current to flow. If thenumber of bars is so small that one or more space harmonic currentscannot flow, then no torque can be produced by those space harmonics inthe stator flux wave.

In a wound rotor induction motor, the number of poles produced by rotorwinding is determined by the winding configuration on the rotor. As aconsequence, torque will be produced by each flux component in thearmature for which there is a corresponding winding having a suitablenumber of poles on the rotor. For purposes of this discussion, thearmature will have a fundamental winding and one or more harmonicwindings. If the rotor has only a fundamental winding, the machine willexperience enhanced torque from the higher armature fundamental fluxdensity component as seen in FIGS. 1C and 1D. However, if the rotorincludes windings having the correct number of poles to interact withthe armature harmonic flux distributions, additional torque can beproduced by each of these flux distributions also.

With respect to synchronous machines, torque is produced by theinteraction of fields produced by the armature excitation with thesteady fields produced by direct current in the field winding. The fieldwinding is typically located on the rotor. Space harmonics in the fluxwave produced by current in the field winding can be produced byproperly shaping the poles in a salient pole machine, or by properlydistributing the field winding in a round-rotor machine. If current inthe field winding produces only a fundamental component of flux density,torque enhancement will result only from the increased armaturefundamental flux component made possible by the harmonic components inthe flux wave. However, for each harmonic component in thefield-produced flux wave which matches a harmonic in the armature fluxwave, further torque enhancement can occur. In a salient polesynchronous machine, if the salient poles are properly shaped, thenadditional torque can be produced by the harmonic components of the fluxwave.

With respect to enhanced performance of any particular machine, anyactual increase in the machine's rating must be determined throughexamination of the factors that initially set the rating, i.e.,electrical heating of the armature winding, electrical heating of therotor winding in an induction machine, electrical heating of the fieldwinding in a synchronous machine, core loss heating of the magneticmembers, and/or mechanical strength of machine components.

Flux distributions as depicted in FIGS. 1C or 1D, can be produced byproviding separate sets of polyphase windings for the fundamental andfor each desired harmonic. Each harmonic, thus, may be applied to adiscrete set of windings. Alternatively, and preferably, however, thefundamental winding will be utilized also for harmonic excitation. Thiscan be done in a variety of ways. For example, in one method ofpracticing the present invention, the outputs of two multiphase powersupplies are coupled together in series to provide fundamental andharmonic excitation of the fundamental winding. Another method utilizesdelta-connected windings coupled together through volt-amp balancers tobalance the potential and currents of both fundamental and harmonicexcitation in the windings. Yet another alternative method utilizes asingle winding with a multiphase inverter, as often found withadjustable speed devices, to inject the harmonic excitations onto thefundamental winding.

Referring now to FIG. 4, therein is depicted in schematic form the crosssection of phase belts for a machine 32 for excitation by fundamental,third harmonic, and fifth harmonic frequencies and the power suppliesfor exciting machine 32. Machine 32 is wound with a two-pole,three-phase fundamental winding 33 which will be excited by fundamentalfrequency supply 26. Third harmonic winding 34 is a six-pole,three-phase winding which will be excited by third harmonic frequencysupply 38. Third harmonic frequency supply 38 will contain phase controlcircuitry as known in the art to assure that the third harmonicfrequency is maintained in the desired phase relationship with thefundamental frequency. Fifth harmonic winding 35 is a ten-pole,three-phase winding which will be excited by fifth harmonic frequencysupply 39 which also contains phase control circuitry.

A specific phase winding in machine 32 will extend between a pair ofletters in a single winding ring, either 33, 34 or 35, indicated by thatletter and its prime. For example, in the winding schematic the phasewinding extending between a and a' in fundamental winding ring 33 is asingle phase fundamental winding. Similarly, the third harmonic windingsa to a' in winding ring 34 represent third harmonic phase belts. Pairsof third harmonic windings may be connected either in series or parallelor may be switched from one connection to the other for ease instarting.

As discussed above, in machine 32 each winding, fundamental winding 33,third harmonic winding 34 and fifth harmonic winding 35, will be excitedby a separate three phase power supply, 26, 38 and 39, respectively. Asdetermined above, the frequency of the third harmonic excitation currentwill be three times the fundamental frequency, and the frequency of thefifth harmonic excitation current will be five times that of thefundamental frequency. The three frequencies will be phase controlled tobe in sync with one another as depicted, for example, in FIG. 1D.

Each harmonic winding must have a number of poles (P_(h)) equal to:

    P.sub.h =np                                                (1)

where:

n is the order of the harmonic (third, fifth, etc.); and

p is the number of poles in the fundamental winding.

For example, for an armature having a fundamental winding having fourpoles (p=4), the third harmonic winding must have 3×4=12 poles. Thefundamental winding will be excited at the fundamental frequency: ω, andeach harmonic winding will be excited at its harmonic of thefundamental, i.e., a third harmonic winding will be excited at theelectrical frequency, 3ω. As will be discussed in more detail laterherein, although the number of phases in the fundamental winding and ineach harmonic winding must be two or more, the number of phases need notbe the same for all windings.

This embodiment allows the greatest flexibility in choosing coil pitchesand numbers of turns for the windings. This construction, however,requires that an armature slot be occupied by at least two differentwindings, thereby resulting in less efficient utilization of the slotarea. Because of the less efficient utilization of the slot area by themultiple windings, this method typically results in less percentageimprovement than do other methods as will be discussed later herein.

For two-phase systems, the displacement of the fundamental and thirdharmonic power supplies are 90 degrees. For three or more phase systems,displacements of the fundamental and the harmonic frequency supplies are360/n electrical degrees for n number of phases.

Because the number of poles for the fundamental will automaticallydetermine the required number of poles for the space harmonic windings,in a machine where separate windings are provided for the fundamentaland for the harmonic excitation currents, the appropriate number ofphases for the harmonic excitation is determined by the number of slotsper pole available for the harmonic windings. Table 1 indicates the slotrequirements of both fundamental and third harmonic windings forpolyphase machines:

                  TABLE 1                                                         ______________________________________                                        PH.sub.f                                                                             S.sub.pf  S.sub.pPHf                                                                           PH.sub.3 S.sub.p3                                                                          S.sub.pPH3                               ______________________________________                                        2       6        3      2        2   1                                        3       6        2      2        2   1                                        6       6        1      2        2   1                                        3       9        3      3        3   l                                        9       9        1      3        3   1                                        2      12        6      2        4   2                                        3      12        4      4        4   1                                        4      12        3      4        4   1                                        6      12        2      4        4   1                                        12     12        1      4        4   1                                        ______________________________________                                    

where:

PH_(f) indicates the number of phases of the fundamental frequency;

S_(pf) indicates the slots per pole required for the fundamentalwinding;

S_(pPHf) indicates the number of slots per pole per phase for thefundamental winding;

PH₃ indicates the number of phases of the third harmonic frequency;

S_(p3) indicates the number of slots per pole required for the thirdharmonic winding; and

S_(pPH3) indicates the number of slots per pole per phase for the thirdharmonic winding.

Those skilled in the art will recognize that in addition to the integralslot per pole per phase distributions indicated in Table 1, fractionalslots per pole per phase may be utilized.

As indicated earlier herein, harmonic frequencies may be injectedthrough use of a single winding for both fundamental and harmonicexcitation. FIG. 5 schematically depicts in winding ring 37 a singlelayer winding for a four-pole, full pitch machine 36 having 36 slots.Machine 36 will preferably be excited by balanced nine-phase fundamentalcurrent. Accordingly, as determined by equation 1, machine 36 will havethree-phase, twelve-pole third harmonic excitation. Fundamental windingsare indicated by the pair of a letter and its prime, with a subscriptindicating the slot position of the winding. For example, the windingbetween, A, in slot 1, and A', in slot 10, is designated as A₁ -A'₁₀.

FIG. 6 depicts the power supply connections to the indicated windings ofmachine 36 of FIG. 5. Transformer secondaries A-I, indicated as 30a,30b, . . . 30i, are the secondaries of one or more transformers coupledto an appropriate nine-phase fundamental frequency power supply. Thoseskilled in the art will recognize that a balanced nine-phase fundamentalfrequency supply may be obtained from a three-phase fundamentalfrequency supply through use of an appropriate number of transformers;typically, three transformers, each with four appropriately woundsecondaries. Third harmonic frequency sources x-z, are preferably thesecondaries of transformers 32x, 32y, and 32z, each coupled to one phaseof a three-phase third harmonic frequency power supply. Alternatively,however, the three-phase third harmonic frequency power supply maycoupled directly to secondaries 30a-30i in the manner indicated. In eacharm of the star connection of FIG. 6, a secondary of the three-phasethird harmonic frequency power supply 32 is coupled between ground and anine-phase fundamental frequency supply secondary 30, and to a pair offundamental windings. The fundamental windings are identified by theslot numbers of machine 36 as indicated in FIG. 5. For example, as shownin FIG. 6, three-phase secondary 32x is coupled in series between groundand nine-phase secondary 30a. The other side of nine-phase secondary 30ais then coupled to windings A₁ -A'₁₀ and to A₁₉ -A'₂₈. In machine 36 ofFIGS. 5 and 6, the winding pairs A₁ -A'₁₀ and A₁₉ -A₂₈ are connected inparallel between nine-phase secondary 30A and ground. Alternatively,winding pairs A₁ -A'₁₀ and A₁₉ -A'₂₈ may be connected in series with oneanother between nine-phase secondary 30a and ground. Such seriesconnection will approximately double the voltage required by machine 36while halving the required current.

Ring 40 in FIG. 5 depicts the third harmonic phasers assigned to eachslot of machine 36. The effective third harmonic excitations shown,(i.e., X₁ -X'₄, X₇ -X'₁₀ ; etc.) do not represent actual windings, butrather the third harmonic phaser distributions achieved throughapplication of power as depicted in FIG. 6 to the fundamental windingsarranged as in FIG. 5.

The present invention may also be employed with a multiple layer windingas opposed to the single layer winding utilized with machine 36 in FIGS.5 and 6. The winding connections for a machine 42 with a double layerwinding are schematically depicted in FIG. 7. Additionally, theprinciples of the present invention may be applied to a machine havingless than a full pitch.

As indicated above, machine 36 of FIGS. 5 and 6 is a four-pole,thirty-six slot, full-pitch machine. A full-pitch machine is preferablefor use with the present invention because an optimal increase inmachine performance is realized through practice of the invention with afull pitch machine. However, those skilled in the art will realize thatthe fundamental excitation of some full pitch machines is more prone togenerate undesirable fifth and seventh harmonics with such a phaserelationship to the fundamental that machine performance is hindered, asdiscussed earlier herein. The coil pitch of a conventional machine istherefore often designed to be 0.83 so as to minimize these undesirablefifth and seventh space harmonics.

The fundamental coil pitch factor is determined by the relationship:

    cos[(full pitch-actual pitch)/full pitch×180/2]      (2)

The third harmonic coil pitch factor for a single winding is determinedby the relationship:

    cos[(full pitch-actual pitch)/full pitch×3×180/2](3)

Table 2 indicates the pitch factors for both the fundamental and thethird harmonic for a double layer winding as determined through use ofequations 2 and 3.

                  TABLE 2                                                         ______________________________________                                                  Per-Unit Fundamental Pitch                                                                           3rd Harmonic                                 Actual pitch                                                                            Pitch    Factor        Pitch Factor                                 ______________________________________                                        9 slots   1.00     1.00          1.00                                         8 slots   0.89     0.98          0.87                                         7 slots   0.78     0.94          0.50                                         6 slots   0.67     0.87          0.00                                         ______________________________________                                    

FIG. 7 depicts a 36 slot machine 42 having a four-pole fundamental and atwelve-pole third harmonic, but with a 0.89 per unit pitch and a doublelayer winding. Windings are represented in FIG. 7 in the same manner aswith FIG. 5, i.e., windings are represented by pairs A₁ -A'₉ ; B₃ -B'₁₁,etc. Phase windings in adjacent pairs of slots, for example A₁ -A'₉ andA₂ -A'₁₀ are connected in parallel. Inner ring 43 does not representactual windings of machine 42, but rather the third harmonic phasedistribution of machine 42. Machine 42 may be excited by powerconnections similar to those depicted in FIG. 6 for machine 36, with theaddition of additional connections to the dual windings in each slot ofmachine 42.

A third method of practicing the present invention involves the use ofvolt-amp balancers. This method allows the use of three-phase powersupplies to provide the fundamental and third harmonic excitation. Withthis method the machine windings are delta-connected. Coupled to eachdelta is one phase of the three phase third harmonic excitation current.Each leg of each delta preferably contains the secondary of atransformer (54a, 54b, 54c; 56a, 56b, 56c; 58a, 58b, 58c in FIG. 10)each of which has a primary coupled to one phase of the third harmonicfrequency power supply. As previously discussed, the frequency of thethird harmonic excitation current will be three times that of thefundamental excitation current.

Autotransformers used in the volt-amp balancers of the power connectionsfor this method will yield variations of resistance andleakage-reactance between full load on the machine and no load. However,for purposes of illustration of this embodiment, ideal conditions areassumed, in which the excitation current, the leakage reactances, andthe resistances of both the volt-amp balancers and the third harmonictransformers are neglected. Under this assumption, the terminal voltageof a winding is equal to the back emf produced by the fundamentalair-gap flux. These ideal conditions assumed are generallyrepresentative of a no load condition of a large rating machine, whoseno load currents are typically small compared to their full loadcurrents.

FIG. 8 depicts the connections and the back emf potential points (A₁,A₂, and A₃) for exciting a machine 45, as depicted in FIG. 9. Machine 45is a four-pole, three-phase machine, having 36 slots and 120° phasebelts. FIG. 10 schematically depicts the particular slot electricalconnections for the connections depicted in FIG. 8. Inner ring 47 ofFIG. 9 depicts the third harmonic phaser distribution of machine 45 whenmachine 45 is excited through the connections as shown in FIGS. 8 and10.

With this volt-amp balancer method of harmonic injection, the number ofphases of the third harmonic is determined by the number of slots perthird harmonic pole by means of the relationship:

    N.sub.ph3 =the smallest multiplier greater than 1 of [n.sub.s /(3×P.sub.f)]                                       (4)

where:

N_(ph3) equals the number of third harmonic phases;

n_(s) equals the number of slots in the machine; and

P_(f) equals the number of poles of the fundamental frequency.

In machine 45 coupled as depicted in FIGS. 8 and 10, 120° phase beltslots 1, 3 and 5, etc. correspond to the three discrete phases of thirdharmonic excitation. Each phase of the three-phase third harmoniccurrent is a zero-sequence current with respect to a particularfundamental delta winding. The back emfs: emf 1, emf 2, and emf 3, ofthe fundamental frequency (in slots 1, 3 and 5, etc.) each have the sameamplitude. Because the phases of these three currents are different,coils in slots 1, 3 and 5, etc. can not be directly connected, either inparallel or in series.

In the connections of FIG. 8, three volt-amp balancers 49a, 49b, and 49care used, one for each phase of the fundamental frequency current. Eachvolt-amp balancer is formed of two autotransformers: T1, indicated as50a, 50b and 50c, and T2, indicated as 52a, 52b and 52c. The turn ratioof transformers T1 (50a, 50b and 50c), is 1:1. The turn ratio of eachtransformer T2 (52a, 52b and 52c), is 2:1. The sides of each transformerT1 will be connected to a terminal potential point A1 or A3 of firstdelta 44 or third delta 48, respectively. Autotransformer T2 will beconnected between terminal potential point A2 of second delta 46 and thecenter tap 53 of its respective transformer T1. Line current of phase Ais coupled to the tap 54a, of autotransformer T2, 52a. Because the turnratio of autotransformer T2 is 2:1 relative to tap 54a, the line currentof phase A will convey one portion to terminal A2 of second delta 46 andtwo portions into center tap 53a of transformer T1, 50a. Similarly,because the turn ratio of each autotransformer (T1) 50a, 50b and 50c is1:1, the current into the terminal potential point A3 of third delta 48is the same as that going into the terminal potential point A1 of firstdelta 44. Accordingly, the line currents entering terminal potentialpoints A1, A2 and A3 of first, second and third deltas 44, 46, and 48,respectively are identical. As a result, the phase current drive will beidentical for each phase.

In operation of the embodiment depicted in FIGS. 8-10, the back emfs atterminal points A1 and A3 are balanced by transformers (T1) 50a, 50b and50c. The potential at terminal potential point A2 and at the center tapof autotransformer T1 are balanced by each auto-transformer T2, 52a, 52band 52c. As indicated above, each third harmonic current appears as azero-sequence current relative to a particular fundamental current.Accordingly, the volt-amp balancers see only the fundamental frequencycurrents and voltages. The back emf voltages are therefore maintained inthe same amplitudes, but in different phases, through operation ofvolt-amp balancers 49a, 49b, 49c. The net effect of this connection isthat the flux wave produced is the same as that which would be producedwith the coils of slots 1, 3 and 5 connected in series.

The fundamental frequency back emf voltage difference between theharmonic phases found in alternate slots, slots 1, 3 and 5, etc., arerelated as shown in the vector diagram of FIG. 11. As can be seen inFIG. 11, the back emfs in each delta 44, 46, 48 are of equal magnitude,but have a phase angle difference of 40°. The volt-amp balancers balancethese phase differences, which occur between alternate slots in machine45. As one skilled in the art can calculate, the total volt-ampererating of volt-amp balancers 49a, 49b and 49c, is 0.37 that of thetransformers required to provide the nine-phase fundamental frequencysupply discussed in relation to the system of FIGS. 5 and 6. The resultsactually achieved with a machine excited through use of volt-ampbalancers will depart somewhat from the ideal performance shown anddescribed. This departure will be due in large part to windingresistance and leakage reactance in the volt-amp balancers and harmonicfrequency transformers. Accordingly, in the design of components for anyparticular system, the transformers for the volt-amp balancers and thirdharmonic excitation should be designed with sufficiently low windingresistance and leakage reactance to minimize departure from the ideal.

FIG. 12 depicts another embodiment of this method of harmonic injectioninto a four-pole, thirty-six slot machine 60, with windingscorresponding to a 60° phase belt connection. The actual connectiondiagram for machine 60 is depicted in FIG. 13. As can be seen in FIG.13, the polarity of each third harmonic transformer 61a, 61b, 61ccoupled to the delta in slot 2 is reversed relative to the polarity ofthird harmonic transformers 63a, 63b, 63c; 65a, 65b, 65c, coupled to thedeltas in slots 1 and 3. The volt-ampere rating of the three volt-ampbalancers 62a, 62b and 62c of FIG. 13 is 0.18 that of the transformersrequired to provide the nine-phase supply discussed in reference to thesystem of FIGS. 5 and 6. The volt-ampere rating of the balancers istherefore substantially less even than that of the system of FIGS. 8-10having 120° phase belt connections.

Another example of the present invention can be illustrated through useof an ideal machine having two third harmonic phases. FIG. 14schematically depicts a three-phase full-pitch, double layer windingsix-pole fundamental, 36 slot machine 66. Referring to the number ofslots per third harmonic pole is: 36/(3×6)=2. Referring to equation 4,because 2 is the smallest multiplier of 2 other than 1, the number ofphases of the third harmonic excitation is 2. Ring 67 depicts the thirdharmonic phase distribution for machine 66.

Referring now also to FIGS. 15 and 16, the windings of machine 66 areconnected in two deltas 69, 71. FIG. 15 depicts the winding fundamentalfrequency back emf potential points (A1 and A2), corresponding to theconnection of the volt-amp balancers 68a, 68b and 68c of FIG. 17. In themachine of FIGS. 14-16, the total volt-amp rating of the three volt-ampbalancers is 0.26 that of the transformers which would be needed tosupply the fundamental frequency excitation through use of a three-phasefundamental frequency supply as discussed in reference to FIGS. 5 and 6.One phase of the third harmonic excitation will be applied to each legof a delta through transformers as depicted at 70 and 72 in FIG. 16.

Because the third harmonic excitation of machine 66 is two phase, oneautotransformer is used for each volt-amp balancer 68a, 68b, 68c. FIG.16 schematically depicts a detailed connection diagram for excitingmachine 66. Each third harmonic frequency supply transformer, 70 and 72,supplies one of the two phases of the third harmonic excitation current.Each transformer 70 and 72 preferably includes a single primary andthree equivalent secondaries, coupled in the deltas as shown. As is wellknown in the art, because each secondary carries one phase of thefundamental frequency current, the mmfs of these fundamental frequencycurrents add to zero, and no fundamental frequency current is induced inthe primary of the third harmonic transformers. This is true of allthird harmonic transformers in all other embodiments described herein.

A fourth method of injection of third harmonic frequencies utilizes asingle stator winding in conjunction with a multiphase inverter.Referring now to FIG. 17, therein is schematically depicted a machine 74having six fundamental poles in thirty-six slots. The windings ofmachine 74 will be connected in two deltas, 78 and 80, displaced 30electrical degrees from one another, each to be excited by a three-phasefundamental frequency supply. Windings indicated by letters enclosed incircles in FIG. 17 represent windings of the second delta as opposed towindings represented by the unencircled letters. For example windingpair A₁ -A'₇ is connected in delta 78, while winding A₂ -A'₈ isconnected in delta 80. Ring 75 depicts the distribution of the thirdharmonic phases in machine 74.

FIG. 18 schematically depicts machine 74 and a multiphase inverter powersupply 76 suitable for use therewith. In the method of this embodiment,neither the multiphase power transformers utilized with the apparatus ofFIGS. 5 and 6, nor the volt-amp balancers of the various apparatus ofFIGS. 7-16 are required. Multiphase inverter 76 provides two three-phasefundamental frequencies 82, 84 each displaced 30° from one another. Thefirst fundamental frequency outputs 82 are coupled to first delta 78,while second fundamental frequency outputs 84 are coupled to seconddelta 80.

The third harmonic excitation is two phase. Each phase is injected intoone of the fundamental delta windings 78, 80. Each leg of each delta,78, 80, will include the secondary 86a, 86b, 86c; 88a, 88b, 88c,respectively, of a transformer having its primary coupled to a thirdharmonic frequency supply. Because this multiphase inverter method ofthe present invention is particularly suitable for use with adjustablefrequency drives, it will be advantageous to generate the third harmonicfrequency directly in response to the fundamental frequency. This may bedone through conventional means. For example, the rectified power 90 maybe applied to a third harmonic frequency generator 92 outputting twophases 94, 96. Third harmonic frequency generator 92 will preferably beresponsive to one phase of a fundamental frequency output 98 to enableprecise frequency and phase control of third harmonic frequency phases94 and 96. Third harmonic frequency phases 94 and 96 will be coupled toprimaries 86', 88' of transformer secondaries 86a, 86b, 86c: and 88a,88b, 88c, respectively.

Each of the above-discussed methods and apparatus allows the optimizingof flux distribution in a polyphase AC machine. As discussed inreference to FIGS. 1-3, the optimal phase relationship will be selectedbetween the harmonic excitation current and the fundamental excitationcurrent to facilitate optimal distribution of the flux density andoptional increases in the total flux per pole of the machine.

Many modifications and variations may be made in the techniques andstructures described and illustrated herein without departing from thespirit and the scope of the present invention. Accordingly, it is to bereadily understood that the embodiments described and illustrated hereinare illustrative only and are not to be considered as limitations forthe present invention.

We claim:
 1. A method of exciting a polyphase alternating currentmachine having a set of windings formed therein wherein at least a firstportion of said winding have a preselected number of poles associatedtherewith, and at least a second portion of said windings have an oddmultiple preselected number of poles associated therewith, comprisingthe steps of:exciting at least said first portion of the windings ofsaid machine with a polyphase fundamental frequency current so that afundamental flux wave rotates in an air gap of said machine at a speedcorresponding to the frequency of said fundamental frequency current;and exciting at least said second portion of the windings of saidmachine with an odd harmonic frequency of said fundamental frequencycurrent so that a harmonic flux wave rotates in the air gap of saidmachine at a speed substantially synchronous with said fundamental fluxwave.
 2. The method of claim 1, wherein said machine is excited by afundamental frequency current by applying said fundamental frequencycurrent to a first set of windings, and wherein said machine is excitedwith an odd harmonic frequency current by applying said odd harmonicfrequency current to a second set of windings.
 3. The method of claim 1,wherein said fundamental frequency current and said harmonic frequencycurrent are applied to single set of windings.
 4. The method of claim 3,wherein the windings in said single set of windings are connected in aplurality of deltas.
 5. The method of claim 4, wherein said deltas arecurrent balanced relative to one another.
 6. The method of claim 4,wherein said deltas are coupled to one another through transformers. 7.The method of claim 6, wherein one phase of said odd harmonic frequencycurrent is applied to each leg of one of said deltas.
 8. A method ofoperating an alternating current machine having a set of windings formedtherein wherein at least a first portion of said windings have apreselected number of poles associated therewith, and at least a secondportion of said windings have an odd multiple preselected number ofpoles associated therewith, comprising the steps of:generating afundamental flow wave in an air gap of said machine by exciting at leastsaid first portion of said windings with a fundamental frequencycurrent; and generating an odd harmonic flux wave in said air gap ofsaid machine by exciting at least said second portion of said windingswith an odd harmonic frequency current of said fundamental frequencycurrent, said harmonic flux wave moving in said air gap in synchronousrelation to said fundamental flux wave.
 9. A polyphase alternatingcurrent machine having at least one set of windings formed therein whereat least a first portion of said windings have a preselected number ofpoles associated therewith, and at least a second portion of saidwindings have an odd multiple preselected number of poles associatedtherewith, comprising:means for exciting at least said first portion ofsaid windings with a polyphase fundamental frequency current to generatea fundamental flux wave rotating in an air gap of said machine; andmeans for exciting at least said second portion of said windings with anodd harmonic frequency current of said fundamental frequency current togenerate a harmonic flux wave rotating in the air gap of said machine insynchronous relation with said fundamental flux wave.
 10. The method ofclaim 9, wherein said machine comprises a first set of windings adaptedfor being excited by said fundamental frequency current and a second setof windings adapted for being excited by said odd harmonic frequencycurrent.
 11. An alternating current machine having a set of windingsformed therein wherein at least a first portion of said windings have apreselected number of poles associated therewith, and at least a secondportion of said windings have an odd multiple preselected number ofpoles associated therewith, comprising:means for generating afundamental flux wave in an air gap of said machine by exciting saidfirst portion of said windings with a fundamental frequency current; andmeans for generating a harmonic flux wave in said air gap of saidmachine by exciting said second portion of said windings with an oddharmonic frequency current of said fundamental frequency current, saidharmonic flux wave moving in said air gap in synchronous relation tosaid fundamental flux wave.
 12. A method for exciting a polyphasealternating current machine to controllably produce a flux wave of apreselected configuration in an air gap of said machine, said machinehaving a set of windings formed therein wherein at least a first portionof said windings have a preselected number of poles associatedtherewith, and at least a second portion of said windings have an oddmultiple preselected number of poles associated therewith, comprisingthe steps of:exciting at least said first portion of said windings witha polyphase fundamental frequency current so that a fundamental fluxwave rotates in the air gap of said machine at a speed corresponding tothe frequency of said fundamental current; exciting at least said secondportion of said windings with an odd harmonic frequency of saidfundamental frequency current, said odd harmonic frequency excitationbeing approximately in phase with said fundamental frequency current sothat an odd harmonic flux wave rotates in the air gap of said machine ata speed substantially identical to the frequency of said fundamentalflux wave; and combining said fundamental and harmonic waves to producea resultant flux wave having a peak amplitude less than the amplitude ofthe fundamental flux wave.
 13. A method, as set forth in claim 12,wherein said step of exciting said machine with a polyphase fundamentalfrequency current includes applying said fundamental frequency currentto a first set of windings, and wherein said step of exciting saidmachine with an odd harmonic frequency includes applying said oddharmonic frequency current to a second set of windings.
 14. A method, asset forth in claim 12, wherein the steps of exciting said machine withthe polyphase fundamental frequency current and the odd harmonicfrequency current includes applying said fundamental frequency currentand said odd harmonic frequency current to a single set of windings. 15.A method for exciting a polyphase alternating current machine tocontrollably produce a flux wave of a preselected configuration in anair gap of said machine, said machine having a set of windings formedtherein wherein at least a first portion of said windings have apreselected number of poles associated therewith, and at least a secondportion of said windings have an odd multiple preselected number ofpoles associated therewith, comprising the steps of:generating afundamental flux wave rotating in the air gap of said machine at a firstpreselected speed by exciting at least said first portion of saidwindings with a polyphase fundamental frequency current; generating anodd harmonic flux wave rotating in the air gap of said machine at saidfirst preselected speed substantially in phase with said fundamentalflux wave by exciting at least said second portion of said windings withan odd harmonic frequency current of said fundamental frequency current;and combining said fundamental and odd harmonic flux waves to produce aresultant flux wave having a peak amplitude less than the amplitude ofthe fundamental flux wave.
 16. A method for exciting a polyphasealternating current machine to controllably produce a flux wave of apreselected configuration in an air gap of said machine having a set ofwindings formed therein wherein at least a first portion of saidwindings have a preselected number of poles associated therewith, and atleast a second portion of said windings have an odd multiple preselectednumber of poles associated therewith, comprising the steps of:generatinga fundamental flux wave rotating in the air gap of said machine at afirst preselected speed by exciting at least said first portion of saidwindings with a polyphase fundamental frequency current; generating anodd harmonic flux wave rotating in the air gap of said machine atsubstantially the same speed as said first preselected speed by excitingat least said second portion of said windings with an odd harmonicfrequency current of said fundamental frequency current; and adjustingthe phase relationship of said harmonic flux wave relative to saidfundamental flux wave to produce a resultant flux wave having a peakamplitude less than the amplitude of the fundamental flux wave.
 17. Anapparatus for exciting a polyphase alternating current machine having atleast one set of stator windings to controllably produce a flux wave ofa preselected configuration in an air gap of said machine, at least afirst portion of said windings having preselected number of polesassociated therewith, and at least a second portion of said windingshaving an odd multiple preselected number of poles associated therewith,comprising:means for exciting at least the first portion of saidwindings with a polyphase fundamental frequency current and generating aresultant fundamental flux wave rotating in the air gap of said machineat a first preselected speed; means for exciting at least the secondportion of said windings with an odd harmonic frequency current of saidfundamental frequency current and generating a resultant odd harmonicflux wave rotating in the air gap of said machine at said firstpreselected speed; and means for adjusting the phase relationship ofsaid harmonic flux wave relative to said fundamental flux wave toproduce a resultant flux wave having a peak amplitude less than theamplitude of the fundamental flux wave.
 18. An apparatus for exciting apolyphase alternating current machine to controllably produce a fluxwave of a preselected configuration in an air gap of said machine,having a set of windings formed therein wherein at least a first portionof said windings have a preselected number of poles associatedtherewith, and at least a second portion of said windings have no oddmultiple preselected number of poles associated therewith,comprising:means for exciting at least said first portion of saidwindings with a polyphase fundamental frequency current so that afundamental flux wave rotates in the air gap of said machine at a speedcorresponding to the frequency of said fundamental current; means forexciting at least said second portion of said windings with an oddharmonic frequency of said fundamental frequency current, said oddharmonic frequency excitation being substantially in phase with saidfundamental frequency current so that an odd harmonic flux wave rotatesin the air gap of said machine at a speed corresponding to the frequencyof said fundamental current, said fundamental and harmonic flux wavescombining to produce an air gap resultant flux wave having a peakamplitude less than the amplitude of the fundamental flux wave.
 19. Anapparatus for exciting a polyphase alternating current machine having atleast one set of stator windings to controllably produce a flux wave ofa preselected configuration in selected portions of said machine, atleast a first portion of said windings having preselected number ofpoles associated therewith, and at least a second portion of saidwindings having an odd multiple preselected number of poles associatedtherewith, comprising:a sinusoidal fundamental frequency current sourceconnected to at least said first portion of said stator windings andadapted for exciting the windings of said machine to produce afundamental flux wave rotating about an air gap in said machine at aspeed corresponding to the frequency of said fundamental frequency; asinusoidal odd harmonic frequency current source connected to at leastsaid second portion of said stator windings and adapted for exciting thewindings of said machine to produce an odd harmonic flux wave rotatingabout the air gap of said machine at a speed substantially synchronouswith said fundamental flux wave; and means for adjusting the phaserelation of said odd harmonic current relative to said fundamentalfrequency current to produce a resultant flux wave having asubstantially rectangular configuration.